Fixed Point Theorems for TSR-Contraction Mapping in Probabilistic Metric Spaces

TL;DR

This paper introduces a new fixed point theorem for TSR-contraction mappings in probabilistic metric spaces, expanding the theoretical framework for fixed point analysis in these spaces.

Contribution

It establishes the existence and uniqueness of fixed points for TSR-contraction mappings, a novel type of contraction in probabilistic metric spaces.

Findings

Proves fixed point existence under TSR-contraction conditions.

Demonstrates the applicability of the new contraction principle.

Extends fixed point theory in probabilistic metric spaces.

Abstract

The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle, namely, TSR-contraction principle in various types of probabilistic metric spaces. The proposed contraction mapping is different from our traditional definitions of contraction mapping.